The premises necessarily lead to the conclusion Or When all the premises are true, the conclusion must be true Or It is impossible to come to a false conclusion when all the premises are true
Examples Either P or Q. Not P, therefore Q. Either Jim or Bob will win the arm wrestle. Jim lost. Therefore Bob won.
If P then Q. P, therefore Q. If Matthew pays the fine, he will get his car back. Matthew pays the fine, therefore he gets his car back.
If P then Q. If Q then R. Therefore, If P then R. If Larry gets the job, he will buy himself a new car. If Larry buys himself a new car, he will need car insurance. Therefore, if Larry gets the job, he will need car insurance.
Incidentally – an argument can be untrue and still be valid, if all the premises logically lead to the conclusion, so:
All cats are reptiles. Bugs Bunny is a cat. Therefore Bugs Bunny is a reptile.
…is absolutely valid, but it isn’t sound (a sound argument is both true and valid)
Invalid Arguments
An argument is invalid if
It is possible for the conclusion to not be true, even when all the premises are true or If the conclusion may be true, but this is only weakly related to the premises.
Examples
Jade Goody was a racist. Jade Goody got cancer. Therefore, being a racist is bad. (the conclusion is true, but has got nothing to do with the premises)
I have always had Nokias and they have never broken on me. Therefore, I will always buy a Nokia. (it may be a good reason to buy a Nokia, but it doesn’t necessarily follow that all Nokias will have be of a similar quality to the phones you’ve had before)
An argument is valid if:
The premises necessarily lead to the conclusion
Or
When all the premises are true, the conclusion must be true
Or
It is impossible to come to a false conclusion when all the premises are true
Examples
Either P or Q. Not P, therefore Q.
Either Jim or Bob will win the arm wrestle. Jim lost. Therefore Bob won.
If P then Q. P, therefore Q.
If Matthew pays the fine, he will get his car back. Matthew pays the fine, therefore he gets his car back.
If P then Q. If Q then R. Therefore, If P then R.
If Larry gets the job, he will buy himself a new car.
If Larry buys himself a new car, he will need car insurance.
Therefore, if Larry gets the job, he will need car insurance.
Incidentally – an argument can be untrue and still be valid, if all the premises logically lead to the conclusion, so:
All cats are reptiles.
Bugs Bunny is a cat.
Therefore Bugs Bunny is a reptile.
…is absolutely valid, but it isn’t sound (a sound argument is both true and valid)
Invalid Arguments
An argument is invalid if
It is possible for the conclusion to not be true, even when all the premises are true
or
If the conclusion may be true, but this is only weakly related to the premises.
Examples
Jade Goody was a racist. Jade Goody got cancer. Therefore, being a racist is bad.
(the conclusion is true, but has got nothing to do with the premises)
I have always had Nokias and they have never broken on me. Therefore, I will always buy a Nokia.
(it may be a good reason to buy a Nokia, but it doesn’t necessarily follow that all Nokias will have be of a similar quality to the phones you’ve had before)